@article{AFST_2004_6_13_1_3_0,
author = {Fabrice Bethuel and Giandomenico Orlandi and Didier Smets},
title = {Motion of concentration sets in {Ginzburg-Landau} equations},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {3--43},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 13},
number = {1},
year = {2004},
zbl = {1063.35075},
mrnumber = {2060028},
language = {en},
url = {https://afst.centre-mersenne.org/item/AFST_2004_6_13_1_3_0/}
}
TY - JOUR AU - Fabrice Bethuel AU - Giandomenico Orlandi AU - Didier Smets TI - Motion of concentration sets in Ginzburg-Landau equations JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2004 SP - 3 EP - 43 VL - 13 IS - 1 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/item/AFST_2004_6_13_1_3_0/ LA - en ID - AFST_2004_6_13_1_3_0 ER -
%0 Journal Article %A Fabrice Bethuel %A Giandomenico Orlandi %A Didier Smets %T Motion of concentration sets in Ginzburg-Landau equations %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2004 %P 3-43 %V 13 %N 1 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/item/AFST_2004_6_13_1_3_0/ %G en %F AFST_2004_6_13_1_3_0
Fabrice Bethuel; Giandomenico Orlandi; Didier Smets. Motion of concentration sets in Ginzburg-Landau equations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 13 (2004) no. 1, pp. 3-43. https://afst.centre-mersenne.org/item/AFST_2004_6_13_1_3_0/
[1] , and , Variational convergence for functionals of Ginzburg-Landau type, preprint 2002.
[2] and , Topological methods for the Ginzburg-Landau equation, J. Math Pures Appl. 11, p. 1-49 (1998). | MR | Zbl
[3] and , A measure theoretic approach to higher codimension mean curvature flow, Ann. Sc. Norm. Sup. Pisa, Cl. Sci. 25, p. 27-49 (1997). | Numdam | MR | Zbl
[4] , , and , W1,p estimates for solutions to the Ginzburg-Landau functional with boundary data in H1/2 , C. R. Acad. Sci. Paris (1) 333, p. 1-8 (2001). | MR | Zbl
[5] , and , Ginzburg-Landau vortices, Birkhäuser, Boston, 1994. | MR | Zbl
[6] , and , Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions, J. Funct. Anal. 186 (2001), p. 432-520. | MR | Zbl
Erratum 188, p. 548-549 (2002). | MR
[7] and , Uniform estimates for the parabolic Ginzburg-Landau equation, ESAIM, C.O.C.V 8, p. 219-238 (2002). | MR | Zbl
[8] , and , Vortex rings for the Gross-Pitaevskii equation, J. Eur. Math. Soc., to appear. | Zbl
[9] , and , Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature, C. R. Acad. Sci. Paris (I) 336, (2003) and preprint Lab. J.L. Lions (2003). | MR | Zbl
[10] and , A minimization problem related to superconductivity, Annales IHP, Analyse Non Linéaire 12, p. 243-303 (1995). | Numdam
[11] and , Travelling waves for the Gross-Pitaevskii equation, Annales IHP, Phys. Théor. 70, (1999). | Numdam | MR | Zbl
[12] , and , On the structure of the Sobolev space H1/2 with values into the circle, C.R. Acad. Sci. Paris (I) 331, p. 119-124, (2000) and detailed paper in preparation. | MR | Zbl
[13] , The motion of a surface by its mean curvature, Princeton University Press (1978). | MR | Zbl
[14] and , Sur une conjecture de E. De Giorgi relative à l'énergie de Ginzburg-Landau, C. R. Acad. Sci. Paris Sér. I Math. 319, p. 167-170 (1994). | MR | Zbl
[15] and , Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics,. J. Differential Equations 90, p. 211-237 (1991). | MR | Zbl
[16] , , Metastable patterns in solutions of u t = ε2uxx - f(u, Comm. Pure Appl. Math. 42, p. 523-576 (1989). | MR | Zbl
[17] , Generation and propagation of interfaces for reaction-diffusion equations, J. Differential Equations 96, p. 116-141 (1992). | MR | Zbl
[18] and , Existence and partial regularity results for the heat flow for harmonic maps, Math. Z. 201, p. 83-103 (1989). | MR | Zbl
[19] , Some conjectures on flow by mean curvature , Proc. of the Capri Workshop ( 1990), Benevento-Bruno-Sbordone (eds.) (1990).
[20] and , Development of interfaces in RN, Proc. Roy. Soc. Edinburgh Sect. A 116, p. 207-220 (1990). | MR | Zbl
[21] , and , Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math. 45, p. 1097-1123 (1992 ). | MR | Zbl
[22] , Geometric Measure Theory, Springer , Berlin, (1969). | MR | Zbl
[23] and , Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math. 38, p. 297-319 (1985). | MR | Zbl
[24] , On a theory of phase transitions with interfacial energy, Arch. Rat. Mech. Anal. 87, p. 187-212 (1985). | MR
[25] , Asymptotic behavior for singularities of the mean curvature flow, J. Diff. Geom. 31, p. 285-299 (1990). | MR | Zbl
[26] , Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature, J. Diff. Geom. 38, p. 417-461 (1993). | MR | Zbl
[27] , Elliptic regularization and partial regularity for motion by mean curvature, Mem. Amer. Math. Soc. 108, no. 520 (1994). | MR | Zbl
[28] and , Dynamics of Ginzburg-Landau vortices, Arch. Rational Mech. Anal. 142, p. 99-125 (1998). | MR | Zbl
[29] and , Scaling limits and regularity results for a class of Ginzburg-Landau systems, Ann. Inst. H. Poincaré Anal. Non Linéaire 16, p. 423-466 (1999). | Numdam | MR | Zbl
[30] and , The Jacobian and the Ginzburg-Landau energy, Calc. Var. PDE 14, p. 151-191 (2002). | MR | Zbl
[31] , Some dynamical properties of Ginzburg-Landau vortices, Comm. Pure Appl. Math. 49, p. 323-359 (1996). | MR | Zbl
[32] , Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds, Comm. Pure Appl. Math. 51, p. 385-441 (1998). | MR | Zbl
[33] and , Complex Ginzburg-Landau equation in high dimension and codimension 2 area minimizing currents, J. Eur. Math. Soc. 1, p. 237-311 (1999). | MR | Zbl
Erratum, Ibid.
[34] and , A quantization property for static Ginzburg-Landau vortices, Comm. Pure Appl. Math. 54, p. 206-228 (2001). | MR | Zbl
[35] and , A quantization property for moving line vortices, Comm. Pure Appl. Math. 54, p. 826-850 (2001). | MR | Zbl
[36] , The topological theory of defects in ordered media, Rev. Modern Phys. 51, p. 591-648 (1979). | MR
[37] , Les minimiseurs locaux pour l'équation de Ginzburg-Landau sont à symétrie radiale, C.R. Acad. Sci. Paris (I) 323, p. 593-598 (1996). | MR | Zbl
[38] , The gradient theory of phase transitions and the minimal interface criterion, Arch. Rat. Mech. Anal. 98, p. 123-142 (1987). | MR | Zbl
[39] and , Un esempio di Γ-convergenza , Boll. Un. Mat. Ital. B 14, p. 285-299 (1977). | MR | Zbl
[40] and , Linear and non linear aspects of vortices , Birkhäuser, (2001). | Zbl
[41] and , Motion of vortex lines in the Ginzburg-Landau model, Phys. D 47, p. 353-360 (1991). | MR | Zbl
[42] , Geometry of measures in Rn: distribution, rectifiability, and densities, Ann. of Math. 125, p. 537-643 (1987). | MR | Zbl
[43] , Line vortices in the U(1) Higgs model, ESAIM, C.O.C.V. 1, p. 77-167 (1996). | Numdam | MR
[44] , Local minimizers for the Ginzburg-Landau energy near critical magnetic fields, I and II, Comm. Contemp. Math. 1, p. 213-254 and p. 295-333 (1999). | MR | Zbl
[45] , Lectures on Geometric Measure Theory, Proc. of the Centre for Math. Anal., Austr. Nat. Univ., 1983 . | MR | Zbl
[46] , Ginzburg-Landau equation and motion by mean curvature. I. Convergence, and II. Development of the initial interface, J. Geom. Anal. 7, no. 3, p. 437-475 and p. 477-491 (1997). | MR | Zbl
[47] , The effect of a singular perturbation on nonconvex variational problems, Arch. Rat. Mech. Anal. 101, p. 209-260 (1988). | MR | Zbl
[48] , On the evolution of harmonic maps in higher dimensions, J. Diff. Geom. 28, p. 485-502 (1988). | MR | Zbl
[49] , On the asymptotic behavior of the Ginzburg-Landau model in 2 dimensions, J. Diff. Equ. 7, p. 1613-1624 (1994), | MR | Zbl
Erratum 8, p. 224 (1995).
[50] , On moving Ginzburg-Landau filament vortices, Max-Planck-Institut Leipzig, preprint.
[51] and , A remark on the multiplicity of solutions for the Ginzburg-Landau equation, Ann. IHP, Analyse Nonlinéaire 16, p. 255-267 (1999). | Numdam | MR | Zbl